As a half-metallocene catalyst for olefin polymerization, dimethylsilyl(tetramethylcyclopentadienyl)(3-tert-butyl-5-methyl-2-phenoxy)titanium dichloride (JP-A 3-163088) and dimethylsilyl(tetramethylcyclopentadienyl) (tert-butylamido)titanium dichloride (JP-A 9-87313) have been respectively disclosed. However, production processes of these transition metal complexes require use of silicon compounds as a key intermediate, which is sensitive to moisture and difficult to be handled. Therefore, a catalyst that can be handled more easily and can afford various olefin polymers has been desired.